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Properties

Label 2.1.4.10a1.3-1.4.28b
Base 2.1.4.10a1.3
Degree \(4\)
e \(4\)
f \(1\)
c \(28\)

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Defining polynomial

$x^{4} + \left(b_{35} \pi^{9} + b_{31} \pi^{8} + b_{27} \pi^{7}\right) x^{3} + \left(b_{26} \pi^{7} + b_{22} \pi^{6} + b_{18} \pi^{5} + a_{14} \pi^{4}\right) x^{2} + \left(b_{33} \pi^{9} + b_{29} \pi^{8} + a_{25} \pi^{7}\right) x + c_{36} \pi^{10} + c_{28} \pi^{8} + \pi$

Invariants

Residue field characteristic: $2$
Degree: $4$
Base field: 2.1.4.10a1.3
Ramification index $e$: $4$
Residue field degree $f$: $1$
Discriminant exponent $c$: $28$
Absolute Artin slopes: $[3,\frac{7}{2},\frac{9}{2},5]$
Swan slopes: $[7,9]$
Means: $\langle\frac{7}{2},\frac{25}{4}\rangle$
Rams: $(7,11)$
Field count: $256$ (complete)
Ambiguity: $4$
Mass: $256$
Absolute Mass: $128$

Diagrams

Varying

These invariants are all associated to absolute extensions of $\Q_{ 2 }$ within this relative family, not the relative extension.

Galois group: $(C_2\times C_4^3):\SD_{16}$ (show 64), $C_2^7.D_8$ (show 64), $(C_2\times C_4^3):D_8$ (show 64), $C_2^7:\SD_{16}$ (show 64) (incomplete)
Hidden Artin slopes: not computed (show 192), $[2,2,\frac{7}{2},\frac{15}{4},\frac{9}{2},\frac{37}{8}]^{2}$ (show 64) (incomplete)
Indices of inseparability: $[53,42,28,16,0]$
Associated inertia: $[1,1,1,1]$
Jump Set: $[1,3,7,15,31]$

Fields

Galois group Galois Artin Indices
Assoc. Inertia Jump Set
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Showing 1-50 of 256

Next   displayed columns for results
Label Polynomial $/ \Q_p$ Galois group $/ \Q_p$ Galois degree $/ \Q_p$ $\#\Aut(K/\Q_p)$ Artin slope content $/ \Q_p$ Swan slope content $/ \Q_p$ Hidden Artin slopes $/ \Q_p$ Hidden Swan slopes $/ \Q_p$ Ind. of Insep. $/ \Q_p$ Assoc. Inertia $/ \Q_p$ Resid. Poly Jump Set
2.1.16.68f1.513 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.514 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.515 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.516 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.517 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.518 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.519 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.520 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.521 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.522 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.523 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.524 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.525 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.526 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.527 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.528 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.529 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.530 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.531 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.532 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.533 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.534 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.535 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.536 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.537 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.538 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.539 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.540 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.541 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.542 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.543 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.544 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.545 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.546 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.547 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.548 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.549 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.550 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.551 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.552 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.553 $x^{16} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.554 $x^{16} + 16 x^{15} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.555 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.556 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.557 $x^{16} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.558 $x^{16} + 16 x^{15} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.559 $x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.560 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{11} + 8 x^{10} + 16 x^{9} + 16 x^{8} + 16 x^{7} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.561 $x^{16} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
2.1.16.68f1.562 $x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 8 x^{10} + 16 x^{6} + 16 x^{5} + 10$ $C_2^7:\SD_{16}$ (as 16T1491) $2048$ $2$ not computed not computed not computed not computed $[53, 42, 28, 16, 0]$ $[1, 1, 1, 1]$ $z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ $[1, 3, 7, 15, 31]$
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